For optical fibers, the index profile is generally qualified in relation to the tracing of the graph plotting the function that associates the refractive index with the fiber radius. Conventionally, the distance r to the center of the fiber is shown along the abscissa, and the difference between the refractive index and the refractive index of the fiber cladding is shown along the ordinate axis. The index profile is therefore referred to as a “step” profile, a “trapezoidal” profile, or a “triangular” profile for graphs having the respective shapes of a step, a trapezoid, or a triangle. These curves are generally representative of the theoretical or set profile of the fiber. The fiber manufacturing stresses may lead to a slightly different profile.
An optical fiber conventionally includes an optical core, whose function is to transmit and possibly to amplify an optical signal, and an optical cladding, whose function is to confine the optical signal within the core. For this purpose, the refractive indexes of the core nc and the outer cladding ng are such that nc>ng. As is well known, the propagation of an optical signal in a single-mode optical fiber decomposes into a fundamental mode guided in the core and into secondary modes (i.e., cladding modes) guided over a certain distance in the core-cladding assembly.
In high bit-rate, wavelength-multiplexed transmission systems, it is advantageous to manage the chromatic dispersion, particularly for rates of 10 Gbits/s or higher. The objective for all multiplex wavelength values is to achieve an accumulated chromatic dispersion that is substantially zero on the link in order to limit pulse broadening. “Accumulated chromatic dispersion” is the integral of the chromatic dispersion with respect to the fiber length; chromatic dispersion being constant, the accumulated chromatic dispersion is equal to the product of the chromatic dispersion multiplied by the length of the fiber. It is also advantageous in the vicinity of the wavelengths used in the system to avoid zero values of the local chromatic dispersion for which the non-linear effects are stronger. Finally, it is also advantageous to limit the accumulated chromatic dispersion slope over the multiplex range so as to avoid or to limit distortions between the multiplex channels. This slope is conventionally the derivative of the chromatic dispersion over the wavelength.
As line fibers for optical fiber transmission systems, single-mode fibers (SMF) or Non-Zero Dispersion Shifted Fibers (NZDSF+) are conventionally employed. NZDSF+ fibers are dispersion shifted fibers having a non-zero, positive chromatic dispersion for the wavelengths at which they are used, typically around 1550 nm.
To compensate the chromatic dispersion and the chromatic dispersion slope in SMF or NZDSF+ fibers used as line fibers, short lengths of Dispersion Compensating Fiber (DCF) can be used. When choosing a DCF, it is generally sought that the ratio of the chromatic dispersion over the dispersion slope of the compensating fiber is substantially equal to that of the line fiber. This ratio is designated by the abbreviation DOS, which stands for Dispersion Over Slope ratio. The smaller the DOS ratio of a transmission fiber, the more difficult it is to compensate the dispersion and the dispersion slope with a DCF.
Also, the chromatic dispersion value for a DCF is not generally a linear function of the wavelength. In contrast, the chromatic dispersion is a substantially linear function of wavelength in line fibers. It is therefore also sought to limit the slope of the slope of the chromatic dispersion, in particular at high bit rates and/or for long-haul transmissions. This slope of the slope is conventionally the second derivative of the chromatic dispersion with respect to the wavelength. In this context the term Residual Dispersion (RD) is given to the value of the chromatic dispersion measured at the end of the line for a given wavelength. Typically, the residual dispersion is zero at a reference wavelength (e.g., 1550 nm) and increases with the wavelengths distant from this reference wavelength owing to a non-zero slope of the chromatic dispersion slope in the compensating fiber. In this context, the term maximum residual dispersion (RDmax) is given to the maximum value of residual dispersion in a spectral band under consideration.
The influence of the slope of the slope of the chromatic dispersion has been identified in the prior art. For example, European Publication No. EP 1,213,595 A (and its counterpart U.S. Pat. No. 6,574,407) propose laying down criteria not only for the dispersion over slope ratio (DOS) of the compensating fiber but also for the ratio of the slope over the slope of the dispersion slope at a wavelength of 1570 nm to reduce the absolute value of the residual chromatic dispersion in the C and L bands. This, however, applies only to a single DCF and is added to the constraint on the ratio of the dispersion over the dispersion slope (DOS). Consequently, this disclosure does not provide a significant reduction in the absolute value of the residual dispersion. In addition, its exemplary fibers possess DOS values of more than 150 nm.
Also, several prior art documents propose combining several portions of different dispersion compensating fibers to reach targeted accumulated values of chromatic dispersion and chromatic dispersion slope.
For example, European Publication No. EP 1,278,316 A1 proposes a dispersion compensating module which includes several compensating fibers having different dispersion and slope values to offset the manufacturing fluctuations of the fibers. Similarly, International Publication No. WO 2002/056069 A2 (and its counterpart U.S. Pat. No. 6,873,798) propose using two compensating fibers having different dispersion and slope values. The article by H. P. Hsu and R. B. Chesler “Trisection Wide Spectral Band Fiber Dispersion Compensation”, IEEE Photonics Technology Letters, Vol. 4, No. 4, April 1992, proposes associating three fibers having different dispersion and slope values to produce a transmission fiber having very low dispersion and dispersion slope values. The slope of the slope of the dispersion is not taken into consideration however in these documents, and a residual dispersion persists.
U.S. Publication No. 2002/0159119 proposes a system for compensating the chromatic dispersion comprising a plurality of compensating fibers to compensate the dispersion and the dispersion slope in the transmission line. This document also proposes taking higher order effects into consideration, and to use as many compensating fibers as orders to be compensated.
The association of several compensating fibers has also been proposed to allow a compensation of chromatic dispersion over several spectral bands. For example, European Publication No. EP 1,383,256 A (and its counterpart U.S. Pat. No. 7,187,824) propose a dispersion compensating module that includes several sub-modules with different compensating fibers to allow a compensation of chromatic dispersion over one or more spectral bands. “Module for Simultaneous C+L Band Dispersion Compensation And Raman Amplification,” (Lars Grüner-Nielsen et al; Article No. TUJ6), presented at the 2002 OFC Conference on Mar. 19, 2002, proposes using a compensating module with two compensating fibers to allow a compensation of chromatic dispersion over the two spectral bands C and L. The slope of the slope of the dispersion, however, is not taken into consideration in these documents, and so a residual dispersion persists.
It has also been established that the lower the DOS ratio, the higher the absolute value of residual dispersion RD on a given spectral band. To achieve a low DOS, the dispersion slope must be relatively high at the reference wavelength. This imposes a slope of the slope that is relatively high. Reference may be made, for instance, to “Impact of Imperfect Wideband Dispersion Compensation on the Performance of WDM Transmission Systems at 40 Gbit/s,” (Jean-Christophe Antona et al; Article No. Th1.6.4), presented at the 2006 ECOC Conference on Sep. 28, 2006. This article reports absolute values of residual dispersion in relation to the DOS value for different compensating fibers.
FIG. 1, which depicts the absolute value of the maximum residual dispersion RDmax for different DOS values in the C+ spectral band (i.e., 1530 nm to 1570 nm), illustrates this finding. The curve shown in a thin dashed line reproduces the absolute value of the maximum residual dispersion obtained with a conventional compensating fiber. The curve shown in a thick solid line reproduces the absolute value of the maximum residual dispersion obtained with the association of two compensating fibers as proposed by the present invention. FIG. 1 clearly shows that with a conventional prior art compensating fiber, the absolute value of the residual dispersion is high when the DOS is low and is non-zero for higher DOS values.